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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 58 · 40 questions
TalentJR

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

NameDateTime takenScore ___ / 40
  1. 1.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 8 (b) 5 (c) 9 (d) 6
  2. 2.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 332 (c) 381 (d) 391
  3. 3.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  5. 5.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 351 (c) 360 (d) 361
  6. 6.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 81 (c) 9 (d) 27
  7. 7.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 36 (c) 108 (d) 39
  8. 8.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 66 (c) 198 (d) 22
  9. 9.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 51 (c) 153 (d) 17
  10. 10.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 60 (c) 171 (d) 57
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 16 (b) 17 (c) 15 (d) 5
  12. 12.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 307 (c) 276 (d) 297
  13. 13.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 18 (c) 162 (d) 57
  14. 14.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  15. 15.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  17. 17.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 97 (c) 88 (d) 98
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 16 (b) 18 (c) 17 (d) 6
  19. 19.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 375 (c) 376 (d) 322
  20. 20.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 496 (c) 486 (d) 495
  21. 21.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 409 (b) 408 (c) 399 (d) 344
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 17 (b) 18 (c) 8 (d) 19
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 65? (a) 6 (b) 12 (c) 13 (d) 10
  24. 24.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 120 (c) 119 (d) 110
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 16 (b) 18 (c) 7 (d) 17
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 16 (b) 18 (c) 17 (d) 6
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 9 (d) 19
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  29. 29.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 113 (b) 114 (c) 104 (d) 122
  30. 30.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 612 (c) 621 (d) 622
  31. 31.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 159 (b) 160 (c) 150 (d) 168
  32. 32.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 216 (c) 75 (d) 24
  33. 33.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  34. 34.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 144 (c) 154 (d) 162
  35. 35.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  36. 36.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 595 (c) 468 (d) 585
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 6 (b) 7 (c) 4 (d) 5
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 18 (b) 7 (c) 17 (d) 19
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 19 (b) 7 (c) 17 (d) 18
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 1 (b) 3 (c) 2 (d) 4

Answer key

  1. 8
  2. 390
  3. 8
  4. 5
  5. 360
  6. 27
  7. 36
  8. 66
  9. 51
  10. 57
  11. 16
  12. 306
  13. 54
  14. 6
  15. 3
  16. 7
  17. 97
  18. 17
  19. 375
  20. 495
  21. 408
  22. 18
  23. 12
  24. 119
  25. 17
  26. 17
  27. 19
  28. 2
  29. 113
  30. 621
  31. 159
  32. 72
  33. 6
  34. 153
  35. 3
  36. 594
  37. 6
  38. 18
  39. 18
  40. 3

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